Money, Credit, and Monetary Policy
|
|
- Albert Cole
- 5 years ago
- Views:
Transcription
1 Money, Credit, and Monetary Policy Te-Tsun Chang Yiting Li January 2013 Abstract We study liquidity e ects and short-term monetary policies in a model with fully exible prices, and with an explicit role for money and nancial intermediation. Banks may hold some deposits and money injections as reserves. If banks hold liquidity bu ers, liquidity e ects exist when the fraction of money injections used to nance spending is larger than that of the initial money stock. The lower the substitutability between newly issued money and the initial money stock, the larger the liquidity e ect. We determine the coe cients of the interest rate rules in response to shocks from the rst-order conditions for a loss function. One implication is that, to minimize the loss caused by uctuations in in ation and output is equivalent to setting the money growth rate at the target in ation rate. If the central bank targets in ation only, the optimal coe cient may depend on the magnitude of the liquidity e ect. J.E.L. Classi cation: E41; E50 Keywords: Liquidity E ects; Money; Credit; Interest Rates; Monetary Policy Te-Tsun Chang: ttchang@ncnu.edu.tw. Yiting Li: yitingli@ntu.edu.tw. We thank Jonathan Chiu, Kevin X.D. Huang, Young Sik Kim, Shouyong Shi, and participants in the 16th International Economic Association World Congress at Bejing and the 2011 Econometric Society Far Eastern South Asian Meeting in Seoul for helpful comments and conversations.
2 1 Introduction As governments across the globe struggle to deal with the aftermath of recent nancial crisis, another major round of nancial regulations has been in the works. A recent Basel III proposal on global banking regulation would require banks to hold liquidity bu ers sizeable enough to enable them to withstand a severe short-term shock. 1 Although Basel III rules will not be fully e ective for several years, we can project what the requirement on liquidity bu ers might imply for the monetary transmission mechanism, and how it will a ect the conduct and e ectiveness of monetary policy. In this paper, we o er a general equilibrium framework to tackle these issues, in line with the macroprudential approach. 2 Our framework features exible prices and frictions, which give rise to the roles of money and nancial intermediation (see, e.g., Lagos and Wright 2005, and Berentsen, Camera, and Waller 2007). Banks channel funds from people with idle cash to those who need liquidity to nance unanticipated consumption. The central bank injects money through nancial intermediaries. Agents make decisions on money holdings before they learn the shocks of preference and money injections. An unexpected money injection increases the nominal amount of loans (the loanable funds e ect); nonetheless, it raises the expected in ation and lowers the real value of money and loans (the Fisher e ect). The existence of a liquidity e ect, where output rises and nominal interest rates fall in response to money supply shocks, depends on whether the loanable funds e ect outweighs in ation expectations. Due to limitations on record keeping, enforcement, and commitment, at money is used as the medium of exchange in the decentralized market. Agents, however, are not subject to the standard cash-in-advance constraint because, before trading, they can borrow cash from banks to supplement their money holdings. The amount that agents can borrow is a ected by the banks 1 The short-term liquidity bu ers (mostly comprising cash, central bank reserves, and domestic sovereign bonds), known as the liquidity coverage ratio, require a bank to have enough highly liquid assets on the balance sheet to cover its net cash out ows over a 30-day period following a shock event, such as a three-notch downgrade to its public credit rating. This will come into e ect in See Basel III: International framework for liquidity risk measurement, standards and monitoring, December As Hanson, Kashyap, and Stein (2011) argue, a framework with microprudential regulations, which is partial equilibrium in its conception and aimed at preventing the costly failure of individual nancial institutions, is limited. Instead, we need a macroprudential approach to recognize the importance of general equilibrium e ects, and safeguard the nancial system as a whole. 1
3 holdings of liquidity bu ers the fraction of deposits and money injections that may be held as reserves, due to regulations or liquidity management considerations. 3 If the fractions of the initial money stock and money injections that are used to nance spending are identical, then the loanable funds e ect o sets the Fisher e ect. Agents make portfolio decisions as if they knew the future money injections. Thus, in contrast to the previous literature, the informational friction in our model does not necessarily generate liquidity e ects. 4 On the other hand, if the fraction of money injections used to nance spending is larger than that of the initial money stock, the loanable funds e ect dominates the Fisher e ect. Consequently, output increases and interest rates fall. In this case, the higher the fraction of money injections used to nance spending, the larger the liquidity e ect. Given that our model identi es conditions for the existence of liquidity e ects, we use it to study a class of short-term monetary policies. Much discussion on monetary policies nowadays is centered on Taylor rules, which specify the nominal interest rate set by the central bank as a reaction function to changes in in ation and output, among other variables. While the coe cients of Taylor rules in conventional New Keynesian models are usually constant (see Woodford 2003), Board sta at the FOMC meeting of November 1995 suggested that equal weights on in ation and the output gap in Taylor rules may not always be appropriate. 5 One may like to know what the optimal reaction coe cients are when an economy faces di erent shocks. We attempt to ask: What are the optimal reaction coe cients when an economy faces di erent shocks? How should the coe cients be determined in an economy with exible prices and frictions as the one we consider here? Following the approach of choosing the reaction coe cients for a target rule as proposed by Svensson (2003), we determine the coe cients of Taylor rules from the rst-order conditions for a speci c loss function. Our model suggests that the central bank should identify the source of in ation when determining the coe cients. If a negative supply shock occurs, the central bank faces 3 Requiring a bank to hold su ciently high liquid assets is a cost on intermediation. Because of less available information on banks net worth, however, developing countries have to rely on the quantitative liquidity regulation (Freedman and Click, 2006; Ratnovski, 2009). 4 For instance, Lucas (1990), Fuerst (1992) and Christano (1991) attribute the reason for the liquidity e ect to agents inability to adjust their portfolios at the time of the money injections. 5 Transcripts of Federal Open Market Committee, les /FOMC meeting.pdf 2
4 a dilemma: trying to control in ation will dampen output, whereas stimulating aggregate demand will escalate in ation. The best strategy is to set a su ciently small coe cient on in ation, which amounts to setting the growth rate of money at the target in ation rate. On the other hand, when a demand shock occurs and pushes up the interest rate, raising the money growth rate to lower the interest rate will cause in ation to rise. To minimize the uctuations in in ation and output, the central bank should choose a su ciently large coe cient on in ation, which is equivalent to setting a su ciently small money growth rate. In the limiting case, the monetary growth rate should be set at the target in ation rate. These two examples thus deliver the same message: the central bank can accomplish more (i.e., minimize the loss) by doing less. Finally, if the central bank targets on in ation only, the optimal coe cient may depend on the magnitude of the liquidity e ect. The current paper is related to two strands of literature on liquidity e ects and Taylor rules. Using a model with segmented markets, Williamson (2004) shows in a model with segmented markets that, if households can issue private money after they learn the shocks to money injections, the liquidity e ect is eliminated. The mechanism in the current paper is similar to Williamson s: bank s lending of money injections, like the private money in Williamson s model, e ectively removes the buyer s cash-in-advance constraint. The distinction is that our paper identify how bank s holding reserves a ects the magnitude of the liquidity e ect, and we discuss short-term monetary policy. In Berentsen and Waller (2011) a stabilization policy generates real e ects because the central bank can commit itself to a price-level path and undo the current money injection at a future date. Our paper di ers in that we do not assume the central bank can undo money injections; moreover, we discuss a class of interest rate rules with which the central bank can minimize the variation of in ation and output. 6 As for studies on the interest rate rule, Alvarez, Lucas, and Weber (2001) use models of segmented markets to show that increasing the interest rate to reduce in ation can be rationalized with quantity-theoretic models of monetary equilibrium. 7 While delivering a similar implication in a model with nancial intermediation and endogenous cash-in-advance constraints, 6 Previous literature using limited participation models to study liquidity e ects includes, for example, Grossman and Weiss (1983), Rotemberg (1984), and Williamson (2006). They identify the distributional e ect of money injections as the underlying mechanism, but often the models are not analytically tractable, except Williamson (2006). 7 The result is similar to Lagos (2011), who shows in a framework of multiple assets that real money balances are reduced by a higher nominal interest rate. He also nds that the optimal monetary policy is a zero interest rate policy the Friedman rule. 3
5 we further determine the coe cients of Taylor rules. 8 The rest of the paper is organized as follows. Section 2 describes the environment. Section 3 derives the equilibrium conditions. In Section 4 we study the liquidity e ect. We discuss issues related to Taylor rules in section 5, and conclude in section 6. 2 The Environment The basic environment is based on Lagos and Wright (2005) and Berentsen, Camera, and Waller (2007). There is a [0; 1] continuum of in nitely lived agents. Time is discrete and continues forever. Each period is divided into two subperiods, and in each subperiod trades occur in competitive markets. There are perishable and perfectly divisible goods, one produced in the rst subperiod, and the other (called the general good) in the second subperiod. The discount factor across periods is = (0; 1); where is the rate of time preference. In the beginning of the rst subperiod, an agent receives a preference shock that determines whether he consumes or produces. With probability an agent can consume but cannot produce; with probability 1 the agent can produce but cannot consume. We refer to consumers as buyers and producers as sellers. This is a simple way to capture the uncertainty of the opportunity to trade. Consumers get utility u(q) from q consumption, where u 0 (q) > 0, u 00 (q) < 0, u 0 (0) = 1 and u 0 (1) = 0. Producers incur disutility c(q) from producing q units of output, where c 0 (q) > 0, c 00 (q) 0. To motivate a role for at money, we assume that all goods trades are anonymous, and there is no public record of individuals trading histories. In the second subperiod, all agents can produce and consume the general good, getting utility U(x) from x consumption, where U 0 (x) > 0, U(x) 00 0, U 0 (0) = 1; and U 0 (1) = 0. Agents can produce one unit of the general good with one unit of labor, which generates one unit of disutility. This setup allows us to introduce an idiosyncratic preference shock while keeping the distribution of money holdings analytically tractable. A government is the sole issuer of at money. The evolution of the money stock is M t = (1 + z t )M t 1, where M t denotes the per capita currency stock, and z t is the money growth rate, in period t: Assume z t = +" t, where is the long-run money growth rate, and " t is a random variable 8 For more studies on Taylor rules, see, e.g., Woodford (2003) for further references. 4
6 with density f on ["; "]: The random variable, " t ; generates a monetary shock, which becomes known at the beginning of period t: In the rst subperiod, the central bank injects money, t = z t M t 1 ; through the banking system, which extends funds to borrowers. This transfer scheme is merely an analytical device to mimic open-market operations. We assume full enforcement, so the central bank can levy nominal taxes to extract cash from the economy, which implies t < 0 and z t < 0. Competitive banks accept nominal deposits and make nominal loans. Sellers in the rst subperiod can deposit their money holdings in banks at the nominal interest rate, i d;t, and are entitled to withdraw funds in the second subperiod. Buyers can borrow money from banks at the nominal loan rate, i b;t ; and repay their loans in the second subperiod. We assume that loans and deposits are not rolled over, and so all nancial contracts are one-period contracts. 9 Moreover, banks have zero net worth, and there are no operating costs. Banks keep records on nancial histories but not on trading histories in the goods market. The record-keeping technology is not available to individuals, so credit between private agents is not feasible. Under the full enforcement of debt repayment, default is not possible. 10 In equilibrium, the loan rate i b;t clears the loan market. Assume that banks are owned by private agents. Because the central bank injects money through nancial intermediaries, banks may have nonzero pro ts. A bank s pro ts are distributed to private agents as dividends, or are withdrawn from agents bank accounts in the case of z t < 0. Moreover, we assume that the central bank injects money equally among banks, and leaves no room for an individual bank to use injections to compete away customers. We consider an economy in which banks may keep a bu er stock of reserves, due to regulations (such as those in the Basel III proposal) or liquidity risk management considerations. A rationale for liquidity risk management is proposed by, for instance, Kashyap, Rajan, and Stein (2002): Banks provide customers with liquidity on demand to satisfy their unexpected needs. Liquidity is provided by o ering demand deposits and loan commitments, which give a borrower the option to take the loans on demand over a certain speci ed period of time. Both of these products require 9 With the assumption on the linear utility costs of production in the second subperiod, agents do not gain by spreading the repayment of loans or redemption of deposits across periods. 10 But see, e.g., Berentsen, Camera, and Waller (2007) and Li and Li (2010), for considering the possibility of default to study the e ects of in ation on credit arrangements, output, and asset prices. 5
7 explicit liquidity risk management. Speci cally, we assume that banks lend out a constant fraction, 2 (0; 1]; of deposits, and a fraction, m 2 (0; 1]; of money that the central bank injects into banks. Though we use regulations and liquidity management considerations to motivate banks holding liquidity bu ers, in Appendix we o er a model with random withdrawal shocks as in the Diamond-Dybvig model to justify banks holding reserves. 11 The timing of events is summarized as follows. At the beginning of the rst subperiod, each agent receives a preference shock. Money injections take place after the realization of preference shocks. Then sellers make deposits and buyers take loans. In the second subperiod, agents settle nancial claims, receive dividends from banks, and adjust money holdings. In section 5, we add demand shocks or supply shocks in the rst subperiod, which occur after the preference shocks but before the money injections. 3 Equilibrium We study symmetric stationary equilibria in which end-of-period real balances are time-invariant; i.e., t 1 M t 1 = t M t ;where t is the value of money in terms of the good produced in the second subperiod. Thus, t 1 t = Mt M t 1 = 1 + z t : As such, the money growth rate, z t ; also represents the in ation rate in the second subperiod of period t: Let V (m t ) denote the expected value from trading in the rst subperiod with m t units of money. Let W (m t ; b t ; d t ) denote the expected value from entering the second subperiod with m t units of money, b t debt, d t deposits, where loans and deposits are in the units of at money. We study a representative period t and work backwards from the second to the rst subperiod, using a similar approach as in Berentsen, Camera, and Waller (2007) to characterize equilibria. The second subperiod In the second subperiod an agent consumes x t ; produces h t goods, redeems deposits, repays 11 Bencivenga and Camera (2011) consider banks and capital in the Lagos-Wright model where depositors make heterogeneous withdrawals, in the spirit of Diamond and Dybvig (1983). Banks, therefore, always hold some positive amount of reserves to satisfy the heterogeneous liquidity needs of buyers. In contrast, banks in our model make loans to satisfy the heterogeneous liquidity needs of agents. 6
8 loans, receives dividends, F t, and adjusts his money holdings. He solves the following problem: W (m t ; b t ; d t ) = max x t;h t;m t+1 U(x t ) h t + E t V (m t+1 ); (1) s.t. x t + t m t+1 = h t + t (m t + F t ) + t (1 + i d;t )d t t (1 + i b;t )b t ; where E t is the expectations operator based on the information of the current period. If an agent has deposited d t in the rst subperiod, he receives (1+i d;t )d t units of money, and if he has borrowed b t ; he should repay (1 + i b;t )b t units of money. Substituting h t from the budget constraint into the objective function, we obtain W (m t ; b t ; d t ) = t (m t + F t ) + t (1 + i d;t )d t t (1 + i b;t )b t The rst order conditions are: + max x t;m t+1 fu(x t ) x t t m t+1 + E t V (m t+1 )g: U 0 (x t ) = 1; (2) E t V m (m t+1 ) t ; = if m t+1 > 0; (3) where V m (m t+1 ) is the marginal value of an additional unit of money taken into the rst subperiod of t + 1: Equation (2) implies x t = x for all agents and for all t: The intertemporal equation (3) determines m t+1 ; independent of the initial holdings of m t when entering the second subperiod. Therefore, the distribution of money holdings is degenerate at the beginning of a period. The envelope conditions are W m = t ; (4) W b = t (1 + i b;t ); (5) W d = t (1 + i d;t ): (6) The rst subperiod Let q b;t and q s;t denote the quantities consumed by a buyer and produced by a seller, respectively, and p t denote the nominal price of the good, in period t: An agent may be a buyer with probability ; spending p t q b;t units of money to get q b;t consumption, or he may be a seller with probability 7
9 1 ; receiving p t q s;t units of money from q s;t production. Because buyers do not make deposits and sellers do not take out loans, in what follows we let b t denote loans taken out by buyers and d t deposits of sellers, and drop these arguments in W (m t ; b t ; d t ) where relevant for notational simplicity. The expected utility of an agent entering the rst subperiod of period t with money holdings m t is V (m t ) = [u(q b;t ) + W (m t + b t p t q b;t ; b t )] + (1 )[ c(q s;t ) + W (m t d t + p t q s;t ; d t )]: (7) Agents trade in a centralized market, so they take the price p t as given. A seller solves max c(q s;t ) + W (m t d t + p t q s;t ; d t ) q s;t;d t s.t. d t m t : Let d;t denote the multiplier on the deposit constraint. The rst order conditions are c 0 (q s;t ) + p t W m = 0; W m + W d d;t = 0: Using (4) and (6) the rst order conditions become p t = c0 (q s;t ) t ; (8) d;t = t i d;t : Equation (8) implies that a seller s production is such that the marginal cost of production, c0 (q s;t) t, equals the marginal revenue, p t : For i d;t > 0, the deposit constraint binds and sellers deposit all money balances; i.e., d t = M t portfolio brought to the rst subperiod. A buyer s problem is 1 : Moreover, the production q s;t is independent of the seller s initial max q b;t ;b t u(q b;t ) + W (m t + b t p t q b;t ; b t ) s.t. p t q b;t m t + b t : 8
10 The buyer faces the cash constraint that his spending cannot exceed his money holdings, m t ; plus borrowing, b t : He should have faced a constraint stating that his borrowing cannot exceed a certain credit limit. However, because banks can force borrowers to repay loans at no cost, the borrowing constraint does not bind; i.e., b t 1; and hence, we ignore this constraint. Let t be the multiplier on the buyer s cash constraint. Using (4), (5), and (8), the rst order conditions are u 0 (q b;t ) = c 0 (q s;t )(1 + t ) t (9) t i b;t = t : (10) If t = 0, (9) reduces to u 0 (q b;t ) = c 0 (q s;t ); implying i b;t = 0: If t > 0, the cash constraint binds, and the buyer spends all of his money; i.e., Combining (9) and (10), we obtain q b;t = m t + b t p t : (11) u 0 (q b;t ) c 0 (q s;t ) = 1 + i b;t; (12) which implies that buyers borrow up to the point at which the marginal bene t of an additional unit of borrowed money, u0 (q b ) c 0 (q s), equals the marginal cost, 1 + i b;t: To nd an agent s optimal money holdings, we take the derivative of (7) with respect to m; and use (4) and (6) to get the marginal value of money: An agent receives u0 (q b;t ) p t V m (m t ; d t ) = u0 (q b;t ) p t + (1 ) t (1 + i d;t ): (13) from spending the marginal unit of money as a buyer, and if he is a seller, he deposits the idle cash in banks, which is valued t (1 + i d;t ) in the second subperiod. Using (3) lagged one period to eliminate V m (m t ; d t ) from (13), an agent s optimal money holdings satisfy E t 1 [ u0 (q b;t ) p t + (1 ) t (1 + i d;t )] t 1 ; = if m t > 0: (14) Condition (14) states that the cost of acquiring an additional unit of money must be greater than the expected discounted bene t, with the equality holding if agents choose to hold money. 9
11 In a symmetric equilibrium, the market-clearing conditions for goods, money, and loan markets are (1 )q s;t = q b;t ; (15) m t = M t 1 ; (16) b t = (1 )d t + m t ; (17) respectively. In the loan market clearing condition, (17), the per capita funds available for banks to lend out include fraction of deposits, (1 capita loans demanded is b t : )d t ; plus m fraction of money injection, while per Finally, banks are perfectly competitive with free entry, so they take as given the loan rate and the deposit rate. There is no strategic interaction among banks or between banks and agents, and no bargaining over the terms of the loan contract. Because the monetary authority injects money into all banks, competitive banks may earn positive pro ts. 12 pro t is! = i b;t b t i d;t (1 )d t + t : Substituting (1 )d t = bt m t a bank s pro t as! = [1 + i d;t m] t + [i b;t A bank s per capita end-of-period from (17), one can rewrite i d;t ]b t: The zero marginal pro t condition implies (see Appendix A2 for the details to derive solutions to the bank s problem): 4 Liquidity E ects i b;t = i d;t : In this section we identify the conditions for the existence of liquidity e ects, and discuss whether the Friedman rule achieves the e cient allocation. An unexpected money injection results in two opposite e ects: it increases the nominal amount of loans that buyers can borrow to spend (loanable funds e ect), whereas it also raises in ation expectations and lowers the future value of money (Fisher e ect). There are liquidity e ects if the loanable funds e ect outweighs the Fisher e ect. The total funds available for each buyer to nance consumption in the rst subperiod include his money holdings, m t ; and the money he borrows from banks, b t : From the loan-market-clearing 12 As argued by Fuerst (1994), there is nothing gained in explicitly modelling the open-market operations since the gains of the loanable reserves would be exactly o set by the loss of the interest-bearing securities. 10
12 condition, (17), we have b t = (1 )d t + m t : (18) Substituting d t = m t ; t = z t M t 1 ; and the market-clearing condition for money, m t = M t 1 ; into (18), we obtain the total funds available per buyer in the rst subperiod: m t + b t = ( + mz t ) M t 1 ; (19) where = + (1 ): Note that is the fraction of the initial money stock, M t 1 ; that can be used to nance spending. In equilibrium the cash constraint binds, i.e., q b;t = mt+bt p t ; from which we derive the relationship between q b;t and the money injection, z t : q b;t c 0 ( q b;t 1 ) = ( + mz t ) t 1 M t 1 ; (20) (1 + z t ) by using (8), (19), and 1 + z t = t 1 : Taking the derivative of (20) with respect to z t ; we obtain t = t 1 M t 1 ( m ) (1 + z t ) 2 [c 0 ( q b;t 1 ) + q b;t 1 c00 ( q b;t 1 )] Observe from (21) that the existence of liquidity e ects t 8 < : > > = 0 if m = 0: < < (21) > 0) depends on whether the fraction of money injections used to nance spending, m ; is larger than that of the initial money stock, : Note that the amount of money used to nance spending and thus, determine the in ation rate, in the rst subperiod is ( + m z t )M t 1 ; whereas the total end-of-period money stock, (1 + z t )M t 1 ; determines the in ation rate in the second subperiod. To see more clearly the underlying mechanism, rewrite (20) as q b;t c 0 ( q b;t 1 ) = (1 + m t z t)m t 1 : (22) It is clear that the term, 1+ m z t ; in (22) captures the money growth rate determining the in ation rate in the rst subperiod, whereas 1 + z t is the money growth rate determining the in ation rate in the second subperiod. If m >, an increase in z t raises the total funds used, and in ation relatively higher than those in the second subperiod market. As a result, the price in the rst subperiod rises more relative to the price in the second subperiod, causing higher incentives to 11
13 produce for sellers. The loanable funds e ect dominates the Fisher e ect, and consequently, output rises by an increase in the growth rate of money. When = m, output is independent of the in ation rate, a result which is di erent from some of the previous studies that also assume uncertainty in trading opportunities (e.g., Lagos and Wright, 2005). The reason is as follows. In this economy, money injections, borrowing, and the rst subperiod goods trade take place within the same subperiod. Though agents make portfolio choices before money injections, buyers can borrow money and agents know the future value of money when they trade in the rst subperiod. Thus, agents make portfolio decisions as if they knew what the future money injections would be. Or, equivalently, it is as if agents could choose money holding in the rst subperiod, and thus, liquidity e ects are eliminated. An immediate implication is that if banks hold no liquidity bu ers ( = m = 1); there is no liquidity e ect. When q b;t rises in response to money injections, interest rates fall. To see this, note that u 0 (q b;t ) = c 0 ( q b;t 1 )(1 + i b;t) from (12) and (15). The case with m > can happen only if banks hold liquidity bu ers. This is so because given m 1 and > 0; < 1 implies < 1: In reality, banks do not lend out all deposits due to regulations or liquidity risk management, whereas often they have no such considerations for the money injected by the central bank. This implies m = 1 > : As a result, the loanable funds e ect dominates the e ect of expected in ation, and money injections increase output and lower nominal interest rates. 13 Note that and m a ect not only the existence but also the magnitude of the liquidity e ect. Equation (21) shows that the magnitude of the liquidity e ect, measured t ; increases in m and decreases in : As the di erence between m and becomes larger, the loanable funds e ect is much stronger than the Fisher e ect, and consequently, the liquidity e ect is larger. One implication is that, given m = 1; unexpected money injections will cause a larger e ect on output and interest rates when banks keep a larger fraction of deposits as reserves. The following proposition summarizes the main results. Proposition 1 If banks hold no liquidity bu ers, liquidity e ects are eliminated. If banks hold 13 In numerical examples, we set u(q b ) = 2q 1 2 b ; c(q s) = q2 s 2 ; = :5; M t 1 = 100; = :11; m = 1 and = :8. As the central bank injects money, e.g., z t increases from :05 to :051, consumption, q b;t, increases from :0: to :858909; and the loan rate, i b;t ; decreases from : to :
14 liquidity bu ers, liquidity e ects exist if and only if the fraction of money injections used to nance spending is larger than that of the initial money stock. In this case, the higher the fraction of money injections used to nance spending, the larger the liquidity e ect. Financial Intermediation and the Friedman Rule. We now show that the Friedman rule achieves the rst-best allocation in our model, in which monetary policy works through nancial intermediaries. 14 When banks lend out all deposits and money injections, the loan rate equals the deposit rate, and from (8) and (12), (14) becomes E t 1 [ t (1 + i d;t )] t 1 : (23) 1 We de ne the average real return on money as 1+ ;i.e., E t 1 t 1 t To implement the Friedman rule in this economy, the policy needs to set the expected return on money equal to the real interest rate; i.e., 1 1+ = 1. From (9) and (10), u0 (q b;t ) = c 0 (q s;t ) when i d;t = 0; and the Friedman rule achieves the e cient allocation. The Friedman rule ensures that agents can perfectly insure themselves against preference shocks because holding currency has zero costs. The Friedman rule also achieves the e cient allocation in an economy where banks hold liquidity bu ers. Given i b;t = i d;t ; the loan rate is larger than the deposit rate. Equation (14) becomes E t 1 t [(1 + i b;t ) + (1 )(1 + i d;t )] t 1 : (24) Under the policy that sets 1 + = ; we obtain u 0 (q b;t ) = c 0 (q s;t ) from (24), as i d;t and i b;t approach to 0. The Friedman rule achieves the e cient allocation. 5 In ation, Interest Rates, and Taylor Rules It is widely accepted that a main goal of monetary policy is to stabilize the price level. 15 There is also a consensus among practitioners that the monetary policy instrument used to achieve this goal should be the short-term interest rate. Economists have focused discussions on a class of strategies 14 Our discussion about the Friedman rule is similar to Berentsen, Camera, and Waller (2005), who consider the real e ect of monetary injections without the banking system. 15 Friedman (1968) said that monetary policy can o set the major disturbances arising from other sources and provide a stable background for the economy. 13
15 known as the Taylor rule (Taylor, 1993), which suggests a simple instrumental rule whereby the monetary authority sets the instrument rate in response to in ation and output gap: i s t = { s + ( t ) + y (y t y t ); (25) where i s t is the instrument rate in period t; { s is the sum of the real interest rate and the target in ation rate, t is the actual in ation rate, is the in ation target, y is (log) output, and y t is (log) potential output. The coe cients in (25), and y ; are positive, which govern the reaction of the central bank. While the coe cients of Taylor rules are assumed constant in many studies, one may wonder whether constant coe cients are optimal when the economy faces di erent shocks. In this section, we tackle this question by determining the coe cients of an instrument rule from the rst-order conditions for a speci c loss function, as suggested by Svensson (2003). We adopt the following approach. First, we study the short-run connections among the money growth rate, in ation, and interest rates. In this economy, the central bank follows an instrument rule with exogenously speci ed coe cients, e.g., the Taylor rule (25). The variables that the central bank targets are the current in ation rate and the output gap, both of which are a ected by shocks. We will show that raising the interest rate to reduce in ation is consistent with reducing the money growth rate, as implied by the quantity theory of money. Then, based on the short-run relationship explored, we will determine the coe cients of the Taylor rule for di erent shocks. To address the issue of how the short-term policy responds to shocks while obtaining analytical results, we assume the following functional forms. The cost function is c(q s;t ) = q2 s;t 2(1+ t), where t is an i:i:d: shock with mean zero and variance 2 < 1: The utility function is u(q b;t ) = (1+ t )q1 b 1, where is the constant coe cient of relative risk aversion, and t is an i:i:d: shock with mean zero and variance 2 < 1. We call t the supply shock, and t the real demand shock. In this section we consider only the commonly observed case in which banks keep some reserves but lend out all money injected by the central bank; i.e., m = 1 > ; so liquidity e ects exist. 5.1 The short-run equilibrium We now explore the short-run connections among the money growth rate, in ation, and interest rates in the face of shocks. Suppose that the central bank uses the loan rate, i s b;t, as the instrument 14
16 rate, and follows the Taylor rule (25). Then, i s b;t is set at i s b;t = + + ( t ) + ( ); (26) 2 where is the potential output. Note that the output gap, log y t log y t, is equal to 1 2 ( t ) under our model speci cations. 16 If current in ation exceeds the targeted in ation, or there exists an output gap ( t > 0), the central bank should raise the interest rate, i s b;t, above its longrun level, +. Assume that 0 < 1 and 0 < 1, where and are exogenous upper bounds of the coe cients. A policy is called active if an increase in in ation by one percentage point prompts the central bank to raise the instrument rate by more than one percentage point ( > 1); and it is called passive if < 1. Without loss of generality, we set = 0 in the following discussion. In this section in ation is measured in terms of the nominal price in the rst subperiod, p t = c 0 (q s;t) t, instead of the nominal price in the second subperiod, 1 t. The reason is that our focus is on how the central bank reacts to shocks, which occur in the demand or supply of goods in the rst subperiod and a ect the market price p t ; whereas t is determined by the total money stock in the second subperiod. Let t pt p t 1 1 denote the in ation rate in the rst subperiod. Then, t ' ( t t 1 ) (z t ) 1 2 (z t 1 ); (27) (See the Appendix for the derivations of equations (27) (29)). In the long run, t = t 1 = = 0, t = ; and (27) implies that the money growth rate equals the target in ation rate, z t = z t 1 =. That is, in the long run, in ation is a monetary phenomenon. In the short-run, however, a money injection or a negative supply shock can lift in ation. To implement the policy, the central bank needs one more equation that describes the behavior of market interest rates. Applying the log-approximation (i.e., log(1 + x) ' x) on (12) and (20), we obtain i b;t = { b;t + t t + (1 + )( 1) (z t ); (28) 2 where { b;t is the long-run average loan rate (note that in the long run t = 0; t = 0 and z t = ). Equation (28) implies that a positive shock from the demand or supply side will raise the interest q q 16 1 In the Appendix we show that q b;t = t 1 M t 1 (1+ t )(+z t ) (1+z t, and q ) s;t = q b;t = t 1 M t 1 (1+ t )(+z t ) 1 1 (1+z t. ) Therefore, the output gap, log y t log y t = log q s;t log q s;t = 1 (t ). 2 15
17 rate. A positive demand shock increases marginal utility, while a positive supply shock reduces the marginal cost and the price; both e ects induce agents to borrow more, and hence, the interest rate rises. 17 Now we have three equations, (26), (27), and (28), to describe the relationship among three variables, f t ; i b;t ; z t g. 18 To study the short-run equilibrium, we focus our attention on the behavior of z t ; from which one can infer the behavior of t and i b;t : Suppose that the market interest rate equals the target rate; i.e., i b;t = i s b;t : Substituting i b;t = i s b;t into (26) and (28), we obtain z t as a rst-order di erence equation: where A z = z t = [( + 1 ) t t t ] (1 + )(1 ) + (1 + ) + A z (z t 1 ); (29) (1 ) (1+ )(1 )+(1+) < 1 is the parameter that captures the lingering e ect of shocks. One can interpret (29) as the epitome of dynamic systems, and use it to understand the e ects of demand or supply shocks on in ation and interest rates. Note that we have a stable solution of z t : the speed of convergence, A z ; is always less than 1; due to the fact that we consider long-run stationary equilibria in which real balances are time invariant. Two factors a ect the lingering e ect: a decrease in or an increase in raises A z. Note that a ects the magnitude of liquidity e ects, and represents the activeness of Taylor rules. If liquidity e ects are stronger (smaller ) or monetary policy is more active (larger ), the e ect of shocks lasts longer (larger A z ), and so it takes more time to achieve the target in ation rate after shocks. The intuitive reason is this. A strong liquidity e ect implies that, a given change in z t will cause a large deviation of in ation from its target level when approaching the long-run equilibrium. Hence, it takes longer for z t to approach its long-run value. We use the following two examples to show that implementing the short-term interest rate rule to reduce in ation is consistent with the quantity theory of money. For the purpose of illustration, suppose that z t 1 = ; t 1 = 0; and initially the central bank sets z t = if no shock occurs. We assume > as in Taylor (1993). 17 From (28) we have the same observation as in Section 4: When banks keep some reserves ( < 1); higher money growth lowers interest rates, but if banks hold no liquidity bu ers, the interest rate does not respond to money injections. 18 In the long run, the money growth rate and the in ation rate equal the target in ation rate,. Substituting z t = t = into (26) and (28), one nds that i b;t = { b = + in the long run. 16
18 First, consider a negative supply shock, t < 0, which lifts in ation and dampens output. The central bank faces a dilemma: it may decrease the instrument rate, i s b;t ; to stimulate output, or increase i s b;t to control in ation. Under the assumption >, the central bank, following the Taylor rule, will increase the target rate. 19 decrease the amount of the money stock, as (28) shows. To raise the interest rate, the central bank has to One can con rm this argument from observing that in (29) z t should fall below when facing a negative supply shock; i.e., z t = ( +1 ) t (1+ )(1 )+(1+) < 0; because > and t < 0: Therefore, raising the interest rate to control in ation is an indirect way of reducing the money supply. When a positive demand shock occurs, t > 0; buyers are eager to consume and borrow from banks, so the loan rate rises, as (28) indicates. The interest rate is o the target, and the central bank increases money supply to drag it down, as implied by (28). While the central bank raises the money growth rate, in ation will climb. According to the interest rate rule implied by (26), the central bank has to raise the target rate in the face of higher in ation. That is, the interest rate will be higher than the original level. 5.2 The determination of the coe cients of Taylor rules When deriving the short-run relationship among z t ; i b;t, and t in Section 5.1, we imposed arbitrary coe cients in the Taylor rule. We now determine the coe cients of Taylor rules from the rstorder conditions of a speci c loss function. First consider a simple form of loss function, which is an equally weighted sum of the squared in ation gap and the squared output gap: L = 1 2 E t[( ) 2 + ^y 2 ]; where ^y is the output gap, and is equal to 1 2 ( t ) under our model speci cations. The loss function can be interpreted as the sum of the variance of in ation and the output gap. We now derive the explicit form of the loss function in this economy. From (27) and (29), the 19 A negative supply shock implies that t = t 2 > 0 from (27). The instrument rate then becomes i s b;t = t + t = t( + ) > 0 because >. 17
19 variances of in ation and monetary shocks, 2 and 2 z; are 2 = (1 + 2 ) 2 z 4 2 ; (30) 2 z = [( + 1 ) ] (1 ) 2 z [(1 + )(1 ) + (1 + ) ] 2 (1 ) 2 2 ; (31) where 2 is the variance of the supply shock, which also equals the variance of the output gap, and z = ( +1 ) (1+ )(1 )+(1+) is the covariance between the money growth and the supply shocks. From (30), 2 is a weighted average of the variances of the supply shock and the monetary shock, and the weight of the latter is related to the magnitude of the liquidity e ects. Note that the variance of the output gap equals the variance of the supply shock, because ^y = 1 2 ( t The loss function thus can be written as: L = 1 2 [ (1 + 2 ) 2 z 4 2 ]: Because the variance of the supply shock cannot be reduced by monetary policies, the only way the central bank can minimize the loss is to reduce the variance of money growth, 2 z. Therefore, we view 2 z as the loss function that the central bank faces, denoted as e L; i.e., the loss function becomes el = 2 z: ). Next we determine the coe cients of Taylor rules in response to supply shocks or demand shocks. The policy maker s problem is to choose the reaction coe cients, and ; to minimize the loss function e L = 2 z. Supply shocks. Consider that a supply shock occurs. Substituting 2 = 0 into (31), we obtain From the rst-order e el = [( + 1 ) ] 2 2 2(1 ) 2 z [(1 + )(1 ) + (1 + ) ] 2 (1 ) 2 2 : (32) + 1 = = 0; we have 2(1 ) [(1 + )(1 ) + (1 + ) ] 2 f( ): (33) 18
20 Substituting (33) into (32), the central bank s problem becomes: [(1 + 2 min f( ) 2 ) 2 2 2(1 ) z ] 2 [(1 + )(1 ) + (1 + ) ] 2 (1 ) 2 2 : The solution is = 0; which, together with (33), implies that = 1 : When a negative supply shock occurs, the central bank faces a dilemma: trying to control in ation decreasing the aggregate demand will dampen output, whereas increasing the aggregate demand to stimulate the economy will escalate the in ation. Our result implies that, to minimize the volatility of in ation and output in this economy, the central bank should set as small as possible. 20 to setting the money growth rate at the target in ation rate, as indicated by (29). This amounts Demand shocks. Now consider that a demand shock occurs. Substituting 2 = z = 0 into (31), we obtain el = [(1 + )(1 )] 2 + 2(1 + )(1 2 ) : Observe e < 0, because < 1: If the demand shock tends to uctuate often and on a large scale, the central bank may intend to choose a su ciently large to minimize the uctuation of in ation. This result can be interpreted as follows. If the central bank sets =, where is the exogenously imposed upper bound of the weight, then from (29), z t = + 2 t (1+ )(1 )+(1+) : The implication is that the central bank, in order to minimize the loss, chooses the smallest possible z t to control in ation. If there were no restrictions on coe cients, the central bank could set an arbitrarily large ; i.e.! 1: This implies that, from (29), the central bank simply sets the money growth rate at the target in ation rate; i.e., z t =. We summarize the results in the following proposition. Proposition 2 Consider the cost function, c(q s;t ) = q2 s;t 2(1+, and the utility function, u(q t) b;t) = (1+ t )q 1 b 1, where t and are i:i:d: shocks. If the central bank follows Taylor rules speci ed in (25), the coe cients that would minimize the volatility of in ation and output gap are (i) = 0 and = 1 when there is a supply shock, and (ii) = when there is a demand shock. 20 In this case, if the central bank follows the policy rule as in Taylor (1993), with coe cients = 1:5 and = 0:5, it will cause higher volatility of in ation. 19
21 As a nal remark, the coe cients and in the above examples do not depend on the magnitude of liquidity e ects; however, it may not be so if we consider other types of Taylor rules. For instance, if the central bank targets in ation only, the optimal coe cient may depend on. To illustrate this point, suppose that the central bank sets the interest rate as i s b;t = + + ( ); and a supply shock occurs. To minimize the loss function, the central bank would choose! 0 as! 0; and! as! The intuitive reason is that when the liquidity e ect is large (small ), a change in the money growth rate will induce a larger change in the interest rate. To minimize the volatility of in ation, therefore, the central bank should set a su ciently small coe cient, : When the liquidity e ect is very small (large ), a large coe cient causes only a slight uctuation of in ation. Actually, according to (29), the central bank should set the money growth rate at the target in ation rate as in previous scenarios. Our result supports Alan Blinder s suggestion that the coe cients in Taylor rules will likely alter if the variables that the central bank targets are changed (FOMC, May, 1995). 6 Conclusion This paper studies liquidity e ects and short-term monetary policies in a model with fully exible prices, and with a explicit role for money and nancial intermediation. We have shown that, if banks hold no liquidity bu ers, money injections a ect in ation but not interest rates or allocation. If banks hold liquidity bu ers, then liquidity e ects exist if and only if the fraction of money injections used to nance spending is larger than that of initial the money stock. The lower the substitutability between newly issued money and the initial money stock, the larger the liquidity e ect. We then apply our framework to determine the reaction coe cients for a class of Taylor rules. Our model suggests that the central bank should identify the source of in ation to choose the coe cients; 21 If = 1, the loss function becomes L e = [(+1 )2 + 2 ]2 2. To minimize the loss L, e the central bank sets 4 2 =. Meanwhile, when = 0, L e = (1 )2 2 2 ; when is minimized at = 1 or = 0. That is, if! 0; (1+ ) 2 (1 ) 2 the central bank sets = 0 to minimize the loss. In the numerical examples, we use the following function form: c(q s;t) = q2 s;t ;u(q 2 b;t) = q1 b ; and we set = 0:5. The optimal coe cient 1 = 0:56; as = 0:2; and = as = 0:8: This implies that, when is relatively small or relatively large, the coe cient increases in. 20
22 however, the policy implications are similar regardless of the source of in ation: the money growth rate should be set at the targeted in ation to minimize the uctuation of in ation. Our paper o ers insights on the implementation of short-term policy; it also illustrates the power and exibility of models that include explicit roles for money and nancial intermediation. 21
23 References Alvarez, F, R. Lucas and W. Weber (2001). Interest Rates and In ation. American Economic Review 91, Bencivenga, V.R. and G. Camera (2011). Banking in a Matching Model of Money and Capital, Journal of Money, Credit and Banking 43, Berentsen, Camera, and Waller (2005). The Distribution of Money Balances and the Nonneutrality of Money, International Economic Review 46, Berentsen, A., G. Camera and C. Waller (2007). Economic Theory 135, Money, Credit and Banking. Journal of Berentsen, A. and C. Waller (2011). Price Level Targeting and Stabilization Policy, Journal of Money, Credit and Banking 43, Christiano, L (1991). Modelling the Liquidity E ect of a Monetary Shock. Federal Reserve Bank of Minneapolis Quarterly Review. Diamond, D. and Dybvig P. (1983). Bank Runs, Deposit Insurance and Liquidit, Journal of Political Economy 91, Friedman, M. (1968). The Role of Monetary Policy. American Economic Review 58, Freedman, P. and R. Click (2006). Banks that don t lend? Unlocking credit to spur growth in developing countries. Development Policy Review 24, Fuerst, T. (1992). Liquidity, Loanable funds and Real activity. Journal of Monetary Economics 29, Fuerst, T. (1994). Monetary Policy and Financial Intermediation. Journal of Money, Credit and Banking 26, Grossman S., and L. Weiss (1983). A Transactions-Based Model of the Monetary Transmission Mechanism. American Economic Review. 73,
24 Hanson, S., A. Kashyap and J. Stein (2011). A Macroprudential Approach to Financial Regulation, Journal of Economic Perspectives, 25, Kashyap, A., R. Rajan and J. Stein (2002). Banks as Liquidity Providers: An Explanation for the Coexistence of Lending and Deposit-Taking. Journal of Finance, Lagos, R. (2011). Asset Prices, Liquidity, and Monetary Policy in an Exchange Economy, Journal of Money, Credit and Banking, 43, Lagos, R. and R. Wright (2005). A Uni ed Framework for Monetary Theory and Policy Analysis. Journal of Political Economy, 113, Li, Y., and Y. Li (2010). Liquidity, Asset Prices, and Credit Constraints, working paper. Lucas, R (1990). Liquidity and the Interest Rates. Journal of Economic Theory, 50, Ratnovski, L. (2009). Bank liquidity regulation and the lender of last resort, Journal of Financial Intermediation, 18, Rocheteau, G. and R. Wright (2010). Liquidity and asset market dynamics, Working Paper 1016, Federal Reserve Bank of Cleveland. Rotemberg, J. (1984). A Monetary Equilibrium Model with Transactions Costs. Journal of Political Economy, 92, Svensson, Lars E. O. (2003). What Is Wrong with Taylor Rules? Using Judgment in Monetary Policy through Targeting Rules, Journal of Economic Literature, 41(2), Taylor, J (1993). Discretion versus Policy Rules in Practice. Carnegie-Rochester Conference Series on Public Policy, 39 (0), Woodford, M., (2003). Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press, Princeton, NJ. Williamson, S. (2004). Limited Participation, Private Money, and Credit in a Spatial Model of Money, Economic Theory, 24,
Liquidity, Asset Price and Banking
Liquidity, Asset Price and Banking (preliminary draft) Ying Syuan Li National Taiwan University Yiting Li National Taiwan University April 2009 Abstract We consider an economy where people have the needs
More informationSupply-side effects of monetary policy and the central bank s objective function. Eurilton Araújo
Supply-side effects of monetary policy and the central bank s objective function Eurilton Araújo Insper Working Paper WPE: 23/2008 Copyright Insper. Todos os direitos reservados. É proibida a reprodução
More informationWORKING PAPER NO OPTIMAL MONETARY POLICY IN A MODEL OF MONEY AND CREDIT. Pedro Gomis-Porqueras Australian National University
WORKING PAPER NO. 11-4 OPTIMAL MONETARY POLICY IN A MODEL OF MONEY AND CREDIT Pedro Gomis-Porqueras Australian National University Daniel R. Sanches Federal Reserve Bank of Philadelphia December 2010 Optimal
More informationBanking, Liquidity Effects, and Monetary Policy
Banking, Liquidity Effects, and Monetary Policy Te-Tsun Chang and Yiting Li NTU, NCNU May 28, 2016 Monetary policy Monetary policy can contribute to offsetting major disturbances in the economy that arise
More informationSearch, Welfare and the Hot Potato E ect of In ation
Search, Welfare and the Hot Potato E ect of In ation Ed Nosal December 2008 Abstract An increase in in ation will cause people to hold less real balances and may cause them to speed up their spending.
More informationCurrency and Checking Deposits as Means of Payment
Currency and Checking Deposits as Means of Payment Yiting Li December 2008 Abstract We consider a record keeping cost to distinguish checking deposits from currency in a model where means-of-payment decisions
More informationBounding the bene ts of stochastic auditing: The case of risk-neutral agents w
Economic Theory 14, 247±253 (1999) Bounding the bene ts of stochastic auditing: The case of risk-neutral agents w Christopher M. Snyder Department of Economics, George Washington University, 2201 G Street
More informationWORKING PAPER NO COMMENT ON CAVALCANTI AND NOSAL S COUNTERFEITING AS PRIVATE MONEY IN MECHANISM DESIGN
WORKING PAPER NO. 10-29 COMMENT ON CAVALCANTI AND NOSAL S COUNTERFEITING AS PRIVATE MONEY IN MECHANISM DESIGN Cyril Monnet Federal Reserve Bank of Philadelphia September 2010 Comment on Cavalcanti and
More informationLiquidity and Asset Prices: A New Monetarist Approach
1 Liquidity and Asset Prices: A New Monetarist Approach 2 Ying-Syuan Li a Yiting Li by a Fu-Jen Catholic University; b National Taiwan University 3 April 2013 4 Abstract 5 6 7 8 9 10 11 When lenders cannot
More informationSTATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013
STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013 Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements,
More informationEndogenous Markups in the New Keynesian Model: Implications for In ation-output Trade-O and Optimal Policy
Endogenous Markups in the New Keynesian Model: Implications for In ation-output Trade-O and Optimal Policy Ozan Eksi TOBB University of Economics and Technology November 2 Abstract The standard new Keynesian
More informationWORKING PAPER NO AGGREGATE LIQUIDITY MANAGEMENT. Todd Keister Rutgers University
WORKING PAPER NO. 6-32 AGGREGATE LIQUIDITY MANAGEMENT Todd Keister Rutgers University Daniel Sanches Research Department Federal Reserve Bank of Philadelphia November 206 Aggregate Liquidity Management
More informationFiscal policy: Ricardian Equivalence, the e ects of government spending, and debt dynamics
Roberto Perotti November 20, 2013 Version 02 Fiscal policy: Ricardian Equivalence, the e ects of government spending, and debt dynamics 1 The intertemporal government budget constraint Consider the usual
More informationIntergenerational Bargaining and Capital Formation
Intergenerational Bargaining and Capital Formation Edgar A. Ghossoub The University of Texas at San Antonio Abstract Most studies that use an overlapping generations setting assume complete depreciation
More informationWeek 8: Fiscal policy in the New Keynesian Model
Week 8: Fiscal policy in the New Keynesian Model Bianca De Paoli November 2008 1 Fiscal Policy in a New Keynesian Model 1.1 Positive analysis: the e ect of scal shocks How do scal shocks a ect in ation?
More informationOptimal Monetary Policy
Optimal Monetary Policy Graduate Macro II, Spring 200 The University of Notre Dame Professor Sims Here I consider how a welfare-maximizing central bank can and should implement monetary policy in the standard
More informationAsset Pricing under Information-processing Constraints
The University of Hong Kong From the SelectedWorks of Yulei Luo 00 Asset Pricing under Information-processing Constraints Yulei Luo, The University of Hong Kong Eric Young, University of Virginia Available
More information1. Money in the utility function (continued)
Monetary Economics: Macro Aspects, 19/2 2013 Henrik Jensen Department of Economics University of Copenhagen 1. Money in the utility function (continued) a. Welfare costs of in ation b. Potential non-superneutrality
More informationLiquidity and Spending Dynamics
Liquidity and Spending Dynamics Veronica Guerrieri University of Chicago Guido Lorenzoni MIT and NBER January 2007 Preliminary draft Abstract How do nancial frictions a ect the response of an economy to
More informationWORKING PAPER NO /R ON THE INHERENT INSTABILITY OF PRIVATE MONEY. Daniel R. Sanches Federal Reserve Bank of Philadelphia
WORKING PAPER NO. 12-19/R ON THE INHERENT INSTABILITY OF PRIVATE MONEY Daniel R. Sanches Federal Reserve Bank of Philadelphia January 2014 On the Inherent Instability of Private Money Daniel R. Sanches
More information1. Cash-in-Advance models a. Basic model under certainty b. Extended model in stochastic case. recommended)
Monetary Economics: Macro Aspects, 26/2 2013 Henrik Jensen Department of Economics University of Copenhagen 1. Cash-in-Advance models a. Basic model under certainty b. Extended model in stochastic case
More informationGrowth and Welfare Maximization in Models of Public Finance and Endogenous Growth
Growth and Welfare Maximization in Models of Public Finance and Endogenous Growth Florian Misch a, Norman Gemmell a;b and Richard Kneller a a University of Nottingham; b The Treasury, New Zealand March
More informationDeterminacy, Stock Market Dynamics and Monetary Policy Inertia Pfajfar, Damjan; Santoro, Emiliano
university of copenhagen Københavns Universitet Determinacy, Stock Market Dynamics and Monetary Policy Inertia Pfajfar, Damjan; Santoro, Emiliano Publication date: 2008 Document Version Publisher's PDF,
More informationReal Wage Rigidities and Disin ation Dynamics: Calvo vs. Rotemberg Pricing
Real Wage Rigidities and Disin ation Dynamics: Calvo vs. Rotemberg Pricing Guido Ascari and Lorenza Rossi University of Pavia Abstract Calvo and Rotemberg pricing entail a very di erent dynamics of adjustment
More informationThe Long-run Optimal Degree of Indexation in the New Keynesian Model
The Long-run Optimal Degree of Indexation in the New Keynesian Model Guido Ascari University of Pavia Nicola Branzoli University of Pavia October 27, 2006 Abstract This note shows that full price indexation
More informationThe Limits of Monetary Policy Under Imperfect Knowledge
The Limits of Monetary Policy Under Imperfect Knowledge Stefano Eusepi y Marc Giannoni z Bruce Preston x February 15, 2014 JEL Classi cations: E32, D83, D84 Keywords: Optimal Monetary Policy, Expectations
More informationFiscal Consolidation in a Currency Union: Spending Cuts Vs. Tax Hikes
Fiscal Consolidation in a Currency Union: Spending Cuts Vs. Tax Hikes Christopher J. Erceg and Jesper Lindé Federal Reserve Board October, 2012 Erceg and Lindé (Federal Reserve Board) Fiscal Consolidations
More informationMonetary Economics Lecture 5 Theory and Practice of Monetary Policy in Normal Times
Monetary Economics Lecture 5 Theory and Practice of Monetary Policy in Normal Times Targets and Instruments of Monetary Policy Nicola Viegi August October 2010 Introduction I The Objectives of Monetary
More informationWorking Paper Series. This paper can be downloaded without charge from:
Working Paper Series This paper can be downloaded without charge from: http://www.richmondfed.org/publications/ On the Implementation of Markov-Perfect Monetary Policy Michael Dotsey y and Andreas Hornstein
More informationInvestment is one of the most important and volatile components of macroeconomic activity. In the short-run, the relationship between uncertainty and
Investment is one of the most important and volatile components of macroeconomic activity. In the short-run, the relationship between uncertainty and investment is central to understanding the business
More informationWORKING PAPER NO MONETARY POLICY IN A CHANNEL SYSTEM
WORKING PAPER NO. 08-7 MONETARY POLICY IN A CHANNEL SYSTEM Aleksander Berentsen University of Basel and Cyril Monnet Federal Reserve Bank of Philadelphia May 6, 2008 Monetary Policy in a Channel System
More informationRevision Lecture. MSc Finance: Theory of Finance I MSc Economics: Financial Economics I
Revision Lecture Topics in Banking and Market Microstructure MSc Finance: Theory of Finance I MSc Economics: Financial Economics I April 2006 PREPARING FOR THE EXAM ² What do you need to know? All the
More informationLecture Notes 1: Solow Growth Model
Lecture Notes 1: Solow Growth Model Zhiwei Xu (xuzhiwei@sjtu.edu.cn) Solow model (Solow, 1959) is the starting point of the most dynamic macroeconomic theories. It introduces dynamics and transitions into
More informationLecture 2, November 16: A Classical Model (Galí, Chapter 2)
MakØk3, Fall 2010 (blok 2) Business cycles and monetary stabilization policies Henrik Jensen Department of Economics University of Copenhagen Lecture 2, November 16: A Classical Model (Galí, Chapter 2)
More informationTechnical Appendix to Long-Term Contracts under the Threat of Supplier Default
0.287/MSOM.070.099ec Technical Appendix to Long-Term Contracts under the Threat of Supplier Default Robert Swinney Serguei Netessine The Wharton School, University of Pennsylvania, Philadelphia, PA, 904
More informationMonetary Policy and the Financing of Firms
Monetary Policy and the Financing of Firms Fiorella De Fiore, y Pedro Teles, z and Oreste Tristani x First draft December 2, 2008 Abstract How should monetary policy respond to changes in nancial conditions?
More informationLiquidity, Monetary Policy, and the Financial Crisis: A New Monetarist Approach
Liquidity, Monetary Policy, and the Financial Crisis: A New Monetarist Approach By STEPHEN D. WILLIAMSON A model of public and private liquidity is constructed that integrates financial intermediation
More informationLiquidity and Asset Prices: A New Monetarist Approach
Liquidity and Asset Prices: A New Monetarist Approach Ying-Syuan Li and Yiting Li May 2017 Motivation A monetary economy in which lenders cannot force borrowers to repay their debts, and financial assets
More informationKeynesian Inefficiency and Optimal Policy: A New Monetarist Approach
Keynesian Inefficiency and Optimal Policy: A New Monetarist Approach Stephen D. Williamson Washington University in St. Louis Federal Reserve Banks of Richmond and St. Louis May 29, 2013 Abstract A simple
More informationThe Transmission of Monetary Policy through Redistributions and Durable Purchases
The Transmission of Monetary Policy through Redistributions and Durable Purchases Vincent Sterk and Silvana Tenreyro UCL, LSE September 2015 Sterk and Tenreyro (UCL, LSE) OMO September 2015 1 / 28 The
More informationComplete nancial markets and consumption risk sharing
Complete nancial markets and consumption risk sharing Henrik Jensen Department of Economics University of Copenhagen Expository note for the course MakØk3 Blok 2, 200/20 January 7, 20 This note shows in
More informationOPTIMAL INCENTIVES IN A PRINCIPAL-AGENT MODEL WITH ENDOGENOUS TECHNOLOGY. WP-EMS Working Papers Series in Economics, Mathematics and Statistics
ISSN 974-40 (on line edition) ISSN 594-7645 (print edition) WP-EMS Working Papers Series in Economics, Mathematics and Statistics OPTIMAL INCENTIVES IN A PRINCIPAL-AGENT MODEL WITH ENDOGENOUS TECHNOLOGY
More informationMonetary Economics. Chapter 5: Properties of Money. Prof. Aleksander Berentsen. University of Basel
Monetary Economics Chapter 5: Properties of Money Prof. Aleksander Berentsen University of Basel Ed Nosal and Guillaume Rocheteau Money, Payments, and Liquidity - Chapter 5 1 / 40 Structure of this chapter
More informationCentral bank credibility and the persistence of in ation and in ation expectations
Central bank credibility and the persistence of in ation and in ation expectations J. Scott Davis y Federal Reserve Bank of Dallas February 202 Abstract This paper introduces a model where agents are unsure
More informationInterest on Reserves, Interbank Lending, and Monetary Policy: Work in Progress
Interest on Reserves, Interbank Lending, and Monetary Policy: Work in Progress Stephen D. Williamson Federal Reserve Bank of St. Louis May 14, 015 1 Introduction When a central bank operates under a floor
More information1 Two Period Production Economy
University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Handout # 3 1 Two Period Production Economy We shall now extend our two-period exchange economy model
More information1 Non-traded goods and the real exchange rate
University of British Columbia Department of Economics, International Finance (Econ 556) Prof. Amartya Lahiri Handout #3 1 1 on-traded goods and the real exchange rate So far we have looked at environments
More information1. Monetary credibility problems. 2. In ation and discretionary monetary policy. 3. Reputational solution to credibility problems
Monetary Economics: Macro Aspects, 7/4 2010 Henrik Jensen Department of Economics University of Copenhagen 1. Monetary credibility problems 2. In ation and discretionary monetary policy 3. Reputational
More informationIntroducing money. Olivier Blanchard. April Spring Topic 6.
Introducing money. Olivier Blanchard April 2002 14.452. Spring 2002. Topic 6. 14.452. Spring, 2002 2 No role for money in the models we have looked at. Implicitly, centralized markets, with an auctioneer:
More informationImperfect Competition, Electronic Transactions, and. Monetary Policy
Imperfect Competition, Electronic Transactions, and Monetary Policy Thanarak Laosuthi Kasetsart University Robert R. Reed y University of Alabama December 4, 202 Abstract In recent years, electronic nancial
More informationSequential Decision-making and Asymmetric Equilibria: An Application to Takeovers
Sequential Decision-making and Asymmetric Equilibria: An Application to Takeovers David Gill Daniel Sgroi 1 Nu eld College, Churchill College University of Oxford & Department of Applied Economics, University
More informationDual Currency Circulation and Monetary Policy
Dual Currency Circulation and Monetary Policy Alessandro Marchesiani University of Rome Telma Pietro Senesi University of Naples L Orientale September 11, 2007 Abstract This paper studies dual money circulation
More informationDepreciation: a Dangerous Affair
MPRA Munich Personal RePEc Archive Depreciation: a Dangerous Affair Guido Cozzi February 207 Online at https://mpra.ub.uni-muenchen.de/8883/ MPRA Paper No. 8883, posted 2 October 207 8:42 UTC Depreciation:
More informationQuantitative Easing at the Zero-Lower Bound
Quantitative Easing at the Zero-Lower Bound In Light of Recent Developments Enrique Martínez-García Federal Reserve Bank of Dallas and Adjunct at Southern Methodist University Dallas, January 30, 205 Abstract
More informationThe Maturity Structure of Debt, Monetary Policy and Expectations Stabilization
The Maturity Structure of Debt, Monetary Policy and Expectations Stabilization Stefano Eusepi Federal Reserve Bank of New York Bruce Preston Columbia University and ANU The views expressed are those of
More informationCredit Frictions and Optimal Monetary Policy
Vasco Cúrdia FRB of New York 1 Michael Woodford Columbia University National Bank of Belgium, October 28 1 The views expressed in this paper are those of the author and do not necessarily re ect the position
More informationDEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES
ISSN 1471-0498 DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES HOUSING AND RELATIVE RISK AVERSION Francesco Zanetti Number 693 January 2014 Manor Road Building, Manor Road, Oxford OX1 3UQ Housing and Relative
More informationOptimal Interest-Rate Rules in a Forward-Looking Model, and In ation Stabilization versus Price-Level Stabilization
Optimal Interest-Rate Rules in a Forward-Looking Model, and In ation Stabilization versus Price-Level Stabilization Marc P. Giannoni y Federal Reserve Bank of New York October 5, Abstract This paper characterizes
More informationComments on \In ation targeting in transition economies; Experience and prospects", by Jiri Jonas and Frederic Mishkin
Comments on \In ation targeting in transition economies; Experience and prospects", by Jiri Jonas and Frederic Mishkin Olivier Blanchard April 2003 The paper by Jonas and Mishkin does a very good job of
More informationThe Effects of Dollarization on Macroeconomic Stability
The Effects of Dollarization on Macroeconomic Stability Christopher J. Erceg and Andrew T. Levin Division of International Finance Board of Governors of the Federal Reserve System Washington, DC 2551 USA
More informationMonetary credibility problems. 1. In ation and discretionary monetary policy. 2. Reputational solution to credibility problems
Monetary Economics: Macro Aspects, 2/4 2013 Henrik Jensen Department of Economics University of Copenhagen Monetary credibility problems 1. In ation and discretionary monetary policy 2. Reputational solution
More informationA Monetary Analysis of Balance Sheet Policies 1
A Monetary Analysis of Balance Sheet Policies Markus Hörmann Federal Ministry of Finance Andreas Schabert 2 University of Cologne This version: December 29, 203 Abstract We augment a standard macroeconomic
More informationPairwise Trade, Payments, Asset Prices, and Monetary Policy
Pairwise Trade, Payments, Asset Prices, and Monetary Policy Ed Nosal Federal Reserve Bank of Chicago Guillaume Rocheteau U.C. Irvine November 17, 2008 Abstract We provide a monetary theory of asset returns
More informationEconomics 135. Course Review. Professor Kevin D. Salyer. June UC Davis. Professor Kevin D. Salyer (UC Davis) Money and Banking 06/07 1 / 11
Economics 135 Course Review Professor Kevin D. Salyer UC Davis June 2007 Professor Kevin D. Salyer (UC Davis) Money and Banking 06/07 1 / 11 Course Review Two goals Professor Kevin D. Salyer (UC Davis)
More informationMonetary Policy: Rules versus discretion..
Monetary Policy: Rules versus discretion.. Huw David Dixon. March 17, 2008 1 Introduction Current view of monetary policy: NNS consensus. Basic ideas: Determinacy: monetary policy should be designed so
More informationExchange Rate Crises and Fiscal Solvency
Exchange Rate Crises and Fiscal Solvency Betty C. Daniel Department of Economics University at Albany and Board of Governors of the Federal Reserve b.daniel@albany.edu November 2008 Abstract This paper
More informationCredit Constraints and Investment-Cash Flow Sensitivities
Credit Constraints and Investment-Cash Flow Sensitivities Heitor Almeida September 30th, 2000 Abstract This paper analyzes the investment behavior of rms under a quantity constraint on the amount of external
More informationIntroducing nominal rigidities.
Introducing nominal rigidities. Olivier Blanchard May 22 14.452. Spring 22. Topic 7. 14.452. Spring, 22 2 In the model we just saw, the price level (the price of goods in terms of money) behaved like an
More informationIncome Distribution and Growth under A Synthesis Model of Endogenous and Neoclassical Growth
KIM Se-Jik This paper develops a growth model which can explain the change in the balanced growth path from a sustained growth to a zero growth path as a regime shift from endogenous growth to Neoclassical
More information1. Money in the utility function (start)
Monetary Policy, 8/2 206 Henrik Jensen Department of Economics University of Copenhagen. Money in the utility function (start) a. The basic money-in-the-utility function model b. Optimal behavior and steady-state
More informationEconomic Growth and Development : Exam. Consider the model by Barro (1990). The production function takes the
form Economic Growth and Development : Exam Consider the model by Barro (990). The production function takes the Y t = AK t ( t L t ) where 0 < < where K t is the aggregate stock of capital, L t the labour
More informationBailouts, Time Inconsistency and Optimal Regulation
Federal Reserve Bank of Minneapolis Research Department Sta Report November 2009 Bailouts, Time Inconsistency and Optimal Regulation V. V. Chari University of Minnesota and Federal Reserve Bank of Minneapolis
More information5. COMPETITIVE MARKETS
5. COMPETITIVE MARKETS We studied how individual consumers and rms behave in Part I of the book. In Part II of the book, we studied how individual economic agents make decisions when there are strategic
More informationResearch Division Federal Reserve Bank of St. Louis Working Paper Series
Research Division Federal Reserve Bank of St. Louis Working Paper Series Scarce Collateral, the Term Premium, and Quantitative Easing Stephen D. Williamson Working Paper 2014-008A http://research.stlouisfed.org/wp/2014/2014-008.pdf
More informationFinancial Market Imperfections Uribe, Ch 7
Financial Market Imperfections Uribe, Ch 7 1 Imperfect Credibility of Policy: Trade Reform 1.1 Model Assumptions Output is exogenous constant endowment (y), not useful for consumption, but can be exported
More informationBehavioral Finance and Asset Pricing
Behavioral Finance and Asset Pricing Behavioral Finance and Asset Pricing /49 Introduction We present models of asset pricing where investors preferences are subject to psychological biases or where investors
More informationScarce Collateral, the Term Premium, and Quantitative Easing
Scarce Collateral, the Term Premium, and Quantitative Easing Stephen D. Williamson Washington University in St. Louis Federal Reserve Banks of Richmond and St. Louis April7,2013 Abstract A model of money,
More informationHuman capital and the ambiguity of the Mankiw-Romer-Weil model
Human capital and the ambiguity of the Mankiw-Romer-Weil model T.Huw Edwards Dept of Economics, Loughborough University and CSGR Warwick UK Tel (44)01509-222718 Fax 01509-223910 T.H.Edwards@lboro.ac.uk
More informationSimple e ciency-wage model
18 Unemployment Why do we have involuntary unemployment? Why are wages higher than in the competitive market clearing level? Why is it so hard do adjust (nominal) wages down? Three answers: E ciency wages:
More informationWORKING PAPER NO BANKING PANICS AND OUTPUT DYNAMICS. Daniel Sanches Research Department Federal Reserve Bank of Philadelphia
WORKING PAPER NO. 17-20 BANKING PANICS AND OUTPUT DYNAMICS Daniel Sanches Research Department Federal Reserve Bank of Philadelphia July 24, 2017 Banking Panics and Output Dynamics Daniel Sanches Federal
More informationConsumption-Savings Decisions and State Pricing
Consumption-Savings Decisions and State Pricing Consumption-Savings, State Pricing 1/ 40 Introduction We now consider a consumption-savings decision along with the previous portfolio choice decision. These
More informationQuasi-Fiscal Policies of Independent Central Banks and Inflation
CAEPR Working Paper #020-2009 Quasi-Fiscal Policies of Independent Central Banks and Inflation Seok Gil Park Indiana University October 30, 2009 This paper can be downloaded without charge from the Social
More informationEmpirical Tests of Information Aggregation
Empirical Tests of Information Aggregation Pai-Ling Yin First Draft: October 2002 This Draft: June 2005 Abstract This paper proposes tests to empirically examine whether auction prices aggregate information
More informationMean-Variance Analysis
Mean-Variance Analysis Mean-variance analysis 1/ 51 Introduction How does one optimally choose among multiple risky assets? Due to diversi cation, which depends on assets return covariances, the attractiveness
More informationLobby Interaction and Trade Policy
The University of Adelaide School of Economics Research Paper No. 2010-04 May 2010 Lobby Interaction and Trade Policy Tatyana Chesnokova Lobby Interaction and Trade Policy Tatyana Chesnokova y University
More information1 Unemployment Insurance
1 Unemployment Insurance 1.1 Introduction Unemployment Insurance (UI) is a federal program that is adminstered by the states in which taxes are used to pay for bene ts to workers laid o by rms. UI started
More informationConditional Investment-Cash Flow Sensitivities and Financing Constraints
Conditional Investment-Cash Flow Sensitivities and Financing Constraints Stephen R. Bond Institute for Fiscal Studies and Nu eld College, Oxford Måns Söderbom Centre for the Study of African Economies,
More informationTrade Agreements as Endogenously Incomplete Contracts
Trade Agreements as Endogenously Incomplete Contracts Henrik Horn (Research Institute of Industrial Economics, Stockholm) Giovanni Maggi (Princeton University) Robert W. Staiger (Stanford University and
More informationFiscal Consolidations in Currency Unions: Spending Cuts Vs. Tax Hikes
Fiscal Consolidations in Currency Unions: Spending Cuts Vs. Tax Hikes Christopher J. Erceg and Jesper Lindé Federal Reserve Board June, 2011 Erceg and Lindé (Federal Reserve Board) Fiscal Consolidations
More informationGeneral Examination in Macroeconomic Theory. Fall 2010
HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examination in Macroeconomic Theory Fall 2010 ----------------------------------------------------------------------------------------------------------------
More informationTOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems III
TOBB-ETU, Economics Department Macroeconomics II ECON 532) Practice Problems III Q: Consumption Theory CARA utility) Consider an individual living for two periods, with preferences Uc 1 ; c 2 ) = uc 1
More informationVolume 35, Issue 4. Real-Exchange-Rate-Adjusted Inflation Targeting in an Open Economy: Some Analytical Results
Volume 35, Issue 4 Real-Exchange-Rate-Adjusted Inflation Targeting in an Open Economy: Some Analytical Results Richard T Froyen University of North Carolina Alfred V Guender University of Canterbury Abstract
More informationMeasuring the Wealth of Nations: Income, Welfare and Sustainability in Representative-Agent Economies
Measuring the Wealth of Nations: Income, Welfare and Sustainability in Representative-Agent Economies Geo rey Heal and Bengt Kristrom May 24, 2004 Abstract In a nite-horizon general equilibrium model national
More informationMoney Inventories in Search Equilibrium
MPRA Munich Personal RePEc Archive Money Inventories in Search Equilibrium Aleksander Berentsen University of Basel 1. January 1998 Online at https://mpra.ub.uni-muenchen.de/68579/ MPRA Paper No. 68579,
More informationThe Liquidity Effect in Bank-Based and Market-Based Financial Systems. Johann Scharler *) Working Paper No October 2007
DEPARTMENT OF ECONOMICS JOHANNES KEPLER UNIVERSITY OF LINZ The Liquidity Effect in Bank-Based and Market-Based Financial Systems by Johann Scharler *) Working Paper No. 0718 October 2007 Johannes Kepler
More informationMonetary Economics: Macro Aspects, 19/ Henrik Jensen Department of Economics University of Copenhagen
Monetary Economics: Macro Aspects, 19/5 2009 Henrik Jensen Department of Economics University of Copenhagen Open-economy Aspects (II) 1. The Obstfeld and Rogo two-country model with sticky prices 2. An
More information1 A Simple Model of the Term Structure
Comment on Dewachter and Lyrio s "Learning, Macroeconomic Dynamics, and the Term Structure of Interest Rates" 1 by Jordi Galí (CREI, MIT, and NBER) August 2006 The present paper by Dewachter and Lyrio
More informationAdaptive Learning in In nite Horizon Decision Problems
Adaptive Learning in In nite Horizon Decision Problems Bruce Preston Columbia University September 22, 2005 Preliminary and Incomplete Abstract Building on Marcet and Sargent (1989) and Preston (2005)
More informationE cient Minimum Wages
preliminary, please do not quote. E cient Minimum Wages Sang-Moon Hahm October 4, 204 Abstract Should the government raise minimum wages? Further, should the government consider imposing maximum wages?
More informationChapters 1 & 2 - MACROECONOMICS, THE DATA
TOBB-ETU, Economics Department Macroeconomics I (IKT 233) Ozan Eksi Practice Questions (for Midterm) Chapters 1 & 2 - MACROECONOMICS, THE DATA 1-)... variables are determined within the model (exogenous
More information